Which cognitive psychology findings are solid that I can use to help students?
matheducators.stackexchange.com
matheducators.stackexchange.com
I think this is a misunderstanding of what "lecturing" is supposed to do. It's supposed to _introduce_ you to the material at a high level. Think of it as of skimming a scientific paper. The actual "learning" is something you do on your own after the lecture (although some lecturers require that you _first_ study the subject and then listen to the lecture), and when doing assignments. IOW, it's not a be all end all, and it shouldn't be treated as the only thing you need to learn the material.
Not for OP, but for typical discussion: A good way of getting people to understand how lecturing is really only introductory is to consider learning a sport. You can get lectured for hours, days, years on technique and strategy and reading the play and knowing your team mates. But pull on the boots or put a racquet in your hand and you're starting from scratch.
"The criticism of practice (called "drill and kill") and the emphasis on sparking interest is very common. But all evidence, from the lab and studies of professionals, indicate that real competence comes with extensive practice. In denying the critical role of practice one is denying children the very thing they need to achieve real competence. The instructional task is not to "kill" motivation by demanding drill, but to find tasks that provide practice while at the same time sustaining interest"
For me it helps that I enjoy perfecting/varying/repeating.
There could be some element of play in math homework. Play is practice that sparks interest. But what is playful math?
“Here’s a character for Pathfinder. Optimize the shit out of it.”
Some of the math learned in high school can be made more fun and playful with applications such as you mentioned, or with contest math designed for high school students. For a few years now I’ve been involved with the CEMC [1] (at my Alma mater) as a grader for the Euclid math contest which I think is quite fun without requiring anything beyond high school math (doesn’t even require calculus).
According to Mentava their program has 5th graders ready for AP math and middle schoolers ready for college computer science.
20 minutes a day.
It’s just another language. A lot of people see it as esoteric wizardry; the debbil in der math, Bobby!
One plus one
1+1
Same thing, less parchment, less writing stick needed. It’s data compression for an era where Walmart didn’t exist
But not in the way teachers/professors teach it. Quite the contrary
I also studied maths as my major (Algebra, to be more precise). Math is infinitely playful. Trying to weasel your way into a hard problem using various results is fun. (Especially if you don't have a fixed deadline that would turn the play into stress.) It is like sitting in an alien workshop and trying very exotic tools that fit other hands.
If you are more of a visual guy, play around with stuff such as fractals. There, you can visualize the intricate structure on your screen. I will never forget the moment when I saw the Mandelbrot set for the first time. Neither probably did Mandelbrot himself; according to the lore, he expected nothing like that and thought that the computer had an error.
It’s like going after a runner’s high though. It takes work to reach that point where you make connections and feel that neurotransmitter rush.
Neurons aren’t special. Electrical state is all over our bodies. Need to use it to trigger the chemistry that builds muscle not just neurons
When I was a sailing instructor, the first day I would always just take kids out on the boat and have fun with very little learning. That gets them invested, and from then on we can teach the necessary skills even when they're boring--tying knots, memorizing vocab, and learning points of sail and right-of-way rules is not what kids think of when they sign up to learn sailing, but it is necessary.
Of course no 12 year old wants to learn geometry or literature when there's no fun, no purpose beyond "this will be useful for you as an adult I promise". They need to be hooked, and then they can go through boring stuff
As far as I understood it, the main limiting factor in education was teachers deliberately holding back knowledge. The main purpose of "problems", and especially of homework, was a show of social submission, designed to persuade the teachers to reveal the next secret. School one essentially one giant hazing ritual.
There's one memory that stands out as the greatest moment in my education. My school had Acorn Archimedes computers, which came with BBC BASIC, and we were allowed to program them during lunch breaks. One of the older students programmed a Space War clone. I very much wanted to write one myself, but I didn't know how to calculate rotations. The older student refused to tell me the secret, which made perfect sense according to my dominance hierarchy model of education.
I begged my math teacher for the secret, and to my surprise he actually explained how to rotate points using trigonometry. This felt like something incredibly subversive, where the teacher was giving me knowledge I hadn't earned. For this reason I still think of that teacher more favorably than any other, despite other teachers objectively doing more for me. I went on to write a superior Space War clone.
Of all the weird misunderstandings kids have about the world, this might be the weirdest I've ever heard.
I'm kinda fascinated, do you recall at what age you believed this? What was the context you grew up in (country, culture, school). Do you recall where the seed of this idea got planted?
I feel this is the most traditional and natural model of education. It's like medieval guilds, where you had literal secrets that would be revealed only after sufficient demonstration of loyalty.
Then in the actual lecture, the teacher would just have a slide deck with exercises. Students tried solving first, then the teacher showed the correct solution. If you got stuck or didn’t understand, you could immediately ask questions, and those questions would also benefit other students’ understanding.
It is hard to understate how much better this method was for grokking the material than the traditional ‘zoning out during the lecture and struggling with the exercises at home’. I don’t understand why all classes aren’t taught this way.
I’m an external examiner for CS students as a side gig. Now that I’ve been one for 8 years, it’s a relatively easy task for me because I’ve been through their curriculum twice every year. I remember the first time, however, and how I subsequently decided I’d better refresh my own… I’m not sure if learning is the right word here, but my own “what I had been taught in CS”. I did so with edx.orc where I took a few Harvard and MIT courses on CS. What struck me about those courses was just how good the video lectures were for me. I have ADHD and bipolar type 2, and I can honestly say I didn’t really do well with CS lectures when I attended university. But these video lectures were so good, that it honestly taught me the first year of introduction and parts of the later courses in a couple of weeks. Sure… I had the foundation with me, but it also made me wonder if you couldn’t just use these lectures everywhere English speaking. Now, I don’t mean to disrespect my own professors but they were terrible at lecturing by comparison. Which isn’t too weird I guess, I imagine it’s natural for some of the top universities in the world to have some of the best lecturers. In this modern age, we can frankly share these awesome video lectures. Lectures you can pause, rewind a bit, rewatch and so on. All the things I would’ve personally benefited from immensely. Then you could have your local professors do the active learning and so on.
I know it’s not likely to happen, but it should.
Having educators is essential for the health of any society. Educators who constantly revise the material, learn it themselves, and teach it to others. Who themselves become informal or formal teachers. This is one of the ways societies deal with change. The educational requirements change with time and place. The teachers themselves are learning all the time. Some are temporarily bad. Some are permanently bad because of bad job incentives or bad evaluation systems.
Replace all this with centrally produced lectures and your society will seriously deteriorate because of the gaps between what needs to be taught at different places and times and what is taught at those places and times will widen considerably.
Please understand that societies are intricate trees and vines, not machines.
I’m not sure a lot of our educators really fall into the latter category. But even if you’re not corporation for the lecture part, at the very least our own educators could do video lectures and make those available. Maybe that might even make some of them improve their teaching styles. When they get to see themselves teach.
Fix those incentives and you won't have to do any of the things you suggest [1]. Good teachers want to teach well, the same way good musicians is always itching to play good music.
[1] Though more but not all lectures should be recorded.
But I could also easily see this backfiring in certain ways. A couple other things that enabled this to be a positive experience:
1) It was a higher level math elective, everyone in that class chose to be a math major and chose to take that particular elective. This avoids having students who simply don't care, which often ruined similar situations in high school in my experience.
2) It was a relatively small class, I think about 15 students, in a relatively small university. Because it was a small school, I already knew most of the other math majors, and the class had a more personable and trusting atmosphere. Even if you didn't know a person, and thought they were stupid or annoying, you didn't want to burn that bridge because you were almost guaranteed to be in a class with them again later. Because of all this, making a mistake was no big deal, even the shyer less-confident students didn't seem particularly nervous.
3) Class attendance and participation was not graded. This made it very clear that doing the problems was for our benefit, it wasn't busy work.
4) You didn't volunteer, and it wasn't an option to sit out. The professor literally was going person-by-person based on how we were seated, starting from a random person each class. This way it wasn't an oppurtunity for know-it-alls to show off, and less motivated and shy students couldn't just disengage
With a slightly different setup it sounds like torture. But as it was, it kept the class engaged and you could immediately apply what you were learning in lecture to cement it.
That was the hardest math class I ever took (discrete and combinatorial mathematics) because--for scheduling reasons--I'd gotten an exception to take it before I'd met the the prereqs, which meant I was a freshman taking this 3000-level elective in parallel with calc 2 lol. If it was with a worse professor I definitely would have failed, I was not at all prepared. I've taken classes with a completely "flipped classroom" and I just don't have the motivation to do well in classes like that, but I also can't focus enough on lectures with no engagement (at least I couldn't back then before I started ADHD medication)
If you only listen to the lecture, and perhaps re-read the notes, you won't learn much. But that's never how a lecture-based course was meant to work!
In my undergrad, it was made clear to us that the learning happens when you do the worksheets, and the discussions around them in the workshops / exercise classes / tutorials / presentations. But the lectures are still there for a reason.
The history of education is littered with the skulls of the failures of pure "discovery learning", sometimes rebranded as "active learning". And apart from a small elite of people who were going to be top of the class whatever you do (short of Vonnegut-style drastic measures), it does. not. work.
The "traditional" method, practiced properly, contains lots of opportunities for practice (which is, naturally, "active") in some sense. It just recognizes that learners sometimes need to be told what to practice, first.
So I guess I don't fully understand the value of lectures, at least not in maths. If I read up on the material, I can go at my own pace.
Of course, everyone learns differently, so YMMV.
The question is therefore not whether lecturing is useful or where does it fit in the overall learning process, but whether those limited hours of prof/TA time are better spent lecturing vs doing something else (e.g. active learning).
There is a trade off between lecturing and active learning, even if you perfectly understand what lecturing is supposed to do.
Which is not bad, but compared to a more coherent program which inspires and empowers students to get interested in the industry and/or maybe in research would be much much much better.
And yes, of course, obviously, of-fucking-course, every year every every stakeholder in this huge circus parrots about this.
And nothing happens. Credentialism and perverse incentives just continue to rob everyone involved of their passions and joy of learning. (Okay, not everyone, but there's a reason that colleges/universities become "easier" https://www.slowboring.com/p/college-students-should-study-m... )
> You can actually model this precisely, mathematically, using a forgetting curve. I'm not exaggerating when I refer to these things as laws of physics
That's utter bullshit. There is no precise model for retention time. It isn't mathematics. It isn't even physics. Retention time isn't even the only factor involved.
So what remains of the "mathematically precise forgetting curve"? People forget more and more over time. And even that isn't 100% true.
It's not mathematical in a precision and mechanical sense, but the standard deviation of practical observations from the modeled curve is low enough to make it a good predictor and guide for spaced repetition and to optimize time spent to retention ratio.
The problem with much psychology (and anything ending in -metrics) is that mainstream research in it, for ~century, has been treating the former and latter as equivalent.
There is no property of animals called, "forgetting", and anything we model with stats is, at best, an epiphenomenon. It's important not let the x-metrics disciplines get away with their pseudo-scientific propaganda on this.
Populations of individuals have, on average, rates of memory (etc.) performance across time which can be approximately quantities. It is highly unlikely this corresponds to any physical property.
Temperature isnt, in this sense, an epiphenomnon.
Your description
> aggregate to an apparent quantity that doesnt correspond to anything in the world
is unclear. What do you mean by "the world"?
You go on to say
> There is no property of animals called, "forgetting"
It feels possible to me that a sufficiently complex model of the brain can observe an individual and determine that they are in a state of "forgetting". Not with current technology, of course, but I don't see what rules it out in principle.
Likewise, I don't see why it's impossible for mental states to be reduced (with sufficient computational power) to the states and interactions of the brain's constituent atoms.
Then there are formula on the other end, "teen mazagine regressions", where the terms are superstitious aggregates (eg., star signs, number of times you've kissed, etc.).
And formula/models/etc. inbetween, where terms like 'temperature' correspond to a property that no part has, but there is a "nearly determinsitic" relationship between them, such that necessarily for any given set of measures (x, y,t) you have a temperature.. but that you cannot, in practice, actually set {(x, y, t)} so you have a "stochastic-causal relationship".
My claim is that almost all pscyho-social science is of the teen magazine variety: running linear regressions on surveys and then falsely attributing reality the apparent property given by the correlation coefficient. This is just outright pseudoscience and why much of this stuff is unreporducible nonesense.
There is nothing even like "temperature" to our mental faculties, which if explained with a scientific theory, would comprise a vast number of specific causal properties. To say we "forget something" is to describe a combination of 100s of processes each of which have different ecological expressions.
Likewise, "IQ" is exactly the same sort of psuedoscience: a linear regression through survey responses of an entire population and then a fraudulent pseudoscientific project of taking this correlation coefficient and turning it into a singular mental faculty. 110% BS
Sometimes it's possible to encode the relationships between these properties using mathematical equations that are falsifiable via experiment. But this isn't what makes something physics. Physics is simply the process of applying this approach to matter, energy and force. I mean, I admit that experimental psychology isn't physics. And we don't yet know the mechanisms well enough to have a model that reduces to fundamental interactions. But it's not far off the way that mathematics is (successfully) used to measure and predict phenomena in other scientific fields such as biology.
You're splitting hairs (quite aggressively) over what is essentially semantics. And the worst part is, you're wrong about the semantics.
I'd advise you to remember the adage that, all models are wrong (whether we're talking about physics or psychology). But some models are -useful-.
We only know that population measures correspond to individual properties because of a highly robust independent theory. In general, almost no ensemble statistics of non-trivial non-experimental phemenomna will work this way. This assumption is called, in statistics, the ecological fallacy.
Applying this assumption that a statistics of surface data of complex systems is like physics is pseudoscience. It's funny, indeed, that you use statistics of particles whose behaviour here is absurdly simple. It is this very assumption which is pseudoscience when applied in general.
My semantics are entirely correct.
Just like how individual people have memory, and their ability to recall things can be measured.
> Their having this property follows from QM, it doesnt not follow from population statistics.
Nope. It's entirely impossible to determine the half life of a substance by observing a single particle, nor can the value be derived mathematically from QM or any other theory. The time it will take for a single particle to decay is random and unpredictable, and the half life can only be determined by looking at population statistics.
Even still, the half life is a real physical property, and it does tell us the percent likelihood for a single particle to decay over a given span of time. And if we (for example) wanted to design an experiment or a mechanism, and we were dealing with an unstable substance, we absolutely could use the half life of that substance to decide the optimal parameters of that experiment (e.g. we can use the half life to assume that a certain approximate amount of radiation will be emitted from the substance over a given period of time).
So I really don't see what is so strange or pseudoscientific about saying that, if we know experimentally that people tend to remember things better under certain conditions, then let's apply those conditions in a classroom in an attempt to have the students retain more information. Your argument is basically that particles are simple and people are not. But that's both irrelevant and subjective.
For conditions that don't generalize. If it would be a "mathematical law", spaced repetition would not work, because the retention time would be that of the last presentation. So, we've got some exception. Interference, reinforcement and generalization are another known influences.
Psychology doesn't have a good model of how memory works, whereas there are fairly detailed approximations to model the behavior of e.g. gases. So it isn't mathematics, and it doesn't approach the standards of physics.
And that's also part of what's wrong with cogsci. It has held physics too long as the standard to emulate.
Thankfully, uncertainty is not an obstacle for acquiring useful knowledge. Not in physics, not in cognitive science.
I understand your skepticism, but you're missing out on a LOT of very useful advancements in our understanding of the brain and mind, despite all uncertainty that still remains.
Based on what that answer is saying, an AI something along the lines of GPT4o - with the ability to lockout YouTube and TikTok and the like - is just going to sky rocket kids learning. Things like Duolingo already are doing the spaced repetition and all that jazz. That stuff is easy enough to handle with software already.
But the accountability portion is key here. We have the hyper addictive apps already now. The kids are successfully hooked. The sugar water is ready for the thirsty rats. Now we just need the supervision, the accountability, the grad student looming above the maze, the gate keeper.
Combining the AIs we already have with the software of spaced repetition and the like should be straightforward. The judgement portion is then essentially solved. All you have to do then is link that output to the ability to access the sugar water, the addictive apps.
The kids are going to do anything to get through these 'lame' educational barriers then.
And all of it will be automated, personalized, and cheap.
Sure, sure, gotta keep an eye on it, spot check things from time to time. Make sure the rascals aren't ginning up the systems and hacking something.
But that is just orders of magnitude cheaper than the near one-on-one instruction that the comment is saying is needed.
Does this also go for programming? Is this an argument for learning academic stuff in academia and not just hands-on vocational group projects?
I tried to use them but haven't really stuck with it.
I know two students who did quite well on step one and step two, but I do not believe they are using Anki now in their residency
I think it's domain dependent.
It's easy to recall things you encounter frequently, and difficult to recall things which are rarely encountered. Failing to recall something means taking the time to look it up.
With spaced repetition, you're making the bet that it's worth spending some time in order to improve recall for a bunch of stuff. -- The surprise is how much value you can get for how little it can cost.
It's likely a good bet for stuff like language learning (or healthsci), where there's a long tail of things you'd like to be able to recall quickly, and 'cost' of looking something up is quite high. (It's not a fluid conversation if you have to bring out a dictionary).
Whereas with e.g. programming, you're often spending time looking stuff up anyway.
Math Academy is awesome. I am a happy customer.
Previous HN comments about it: https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...
[0] https://www.amazon.com/Make-Stick-Science-Successful-Learnin...
Here's the HN post on the review:
Outsmart Your Brain: Why Learning Is Hard and How You Can Make It Easy:
This question definitely does not pertain to the subject of the answer specifically but rather these Stack Exchange posts I see on here from time: this answer is so in-depth, so well written and so informative, it could be an entire article in a neuroscience magazine. Who goes to these kinds of lengths to post an answer on a niche Stack Exchange question? And why?
In the real world is not necessarily important to be able to rattle off information off the top of your head. More import is simply knowing that a thing exists, so you can go and look it up. Lectures are good at providing the latter.
That’s not true of course, but motivation is key. Do they actually read the books, do they solve the problems themselves? Or do they read the summary before filling in the multiple choice question? The first stimulates learning, the latter temporary memorization
EDIT: there are a number of other studies on google scholar linking ADHD to psychopathy (in prison populations), just not the one with the fMRI scans.
https://supermemo.guru/wiki/SuperMemo_does_not_work_for_kids
The title is a bit exaggerated. Spaced repetition should work fine for adolescents, it probably doesn’t work for very young children, and for the ages 5-10 it’s going to need some adaption.
Spaced repetition is a trick to get the adult brain to retain knowledge, something it does not do easily. Adults are optimized to forget daily life (what did you have for lunch yesterday?), but to remember sporadic and important events, things that have may impact on survival. Spaced repetition tricks the adult mind into thinking that your daily Spanish vocab is important because you didn’t test today’s word for three months.
Younger children are different. Their greater plasticity means that they can learn languages without much conscious effort, as long as the volume of information is high enough. A child doesn’t learn a language 10 words a day like an adult does. It may be volume rather than spacing that is more important in children.
In fact, it has been hypothesized (Krashen’s input hypothesis) that adults also acquire language subconsciously through input. We just spend less time on it than children.
Younger children are different. Their greater plasticity means that they can learn languages without much conscious effort, as long as the volume of information is high enough. A child doesn’t learn a language 10 words a day like an adult does. It may be volume rather than spacing that is more important in children.
A friend of mine did the same at 8.
If they have any issues: depression, low energy, adhd, bipolar disorder, schizophrenia, ...?
It might be beneficial to those people, to try an elimination diet.
The idea I got eventually is this: We've all been wrecking our guts with fast food and unknown chemicals, so everyone is affected to a certain degree. Here's my collection, feel free to add articles if you find something related.
https://github.com/cutestuff/FoodDepressionConundrum/blob/ma...
Many students are demoralized by school because schooling doesn't bother telling kids why they are learning something.
In elementary school, when the teacher stepped into the hallway, a common complaint to hear was "what's the point of this?"
By middle and high school, the question became a mindset - "this is pointless."
School have know close to maximum learning for 100 years. Most of school is fluff. Better learning, or more efficient learning won't change it.
By far the largest issue currently is behavioral problems and worsening situation dealing with them.
This is bad students making good students fail.
Within the confines of what's currently allowed and dealing with politicians, drugging bad students seems the best solution.
The problem is good students are also being drugged.
The cognitive psychology solution is convincing parents of good students not to drug their kids.